Geodesic
ON BI-HARMONIC HYPERSURFACES IN EUCLIDEAN SPACE OF ARBITRARY DIMENSION
Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 633-642

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DOI

The following Chen's bi-harmonic conjecture made in 1991 is well-known and stays open: The only bi-harmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we prove that the bi-harmonic conjecture is true for bi-harmonic hypersurfaces with three distinct principal curvatures of a Euclidean space of arbitrary dimension. 
GUPTA, RAM SHANKAR. ON BI-HARMONIC HYPERSURFACES IN EUCLIDEAN SPACE OF ARBITRARY DIMENSION. Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 633-642. doi: 10.1017/S0017089514000524
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     author = {GUPTA, RAM SHANKAR},
     title = {ON {BI-HARMONIC} {HYPERSURFACES} {IN} {EUCLIDEAN} {SPACE} {OF} {ARBITRARY} {DIMENSION}},
     journal = {Glasgow mathematical journal},
     pages = {633--642},
     year = {2015},
     volume = {57},
     number = {3},
     doi = {10.1017/S0017089514000524},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000524/}
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